The sound field generated by tethered stingless bees ...jeb.biologists.org/content/jexbio/211/5/686.full.pdf · bee foragers of the genus Melipona generate pulsed thorax vibrations

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INTRODUCTIONIn the analysis of communication systems, knowledge of the physicalnature of the signals transmitted is of fundamental importance andrepresents an important step towards the identification of potentialreceivers. When collecting at highly profitable nectar sources, stinglessbee foragers of the genus Melipona generate pulsed thorax vibrationsupon their return to the nest. In all cases studied so far, the temporalpattern of these vibrations predominantly and highly significantlycorrelated with the sugar concentration of the collected food (Hrnciret al., 2006a). There are three potential pathways for the transmissionof this information to prospective recruits: (i) direct contact duringtrophallaxis (Hrncir et al., 2006b), (ii) substrate vibrations (Lindauerand Kerr, 1958), and (iii) airborne sounds (Esch, 1967; Nieh, 1998;Nieh et al., 2003). So far, only pathways (i) and (ii) have beeninvestigated in some detail in Melipona bees (Hrncir et al., 2000;Hrncir et al., 2006b; Hrncir, 2003; Morawetz, 2007; Morawetz et al.,2007).

Current knowledge of the transformation of thoracic vibrationsto airborne sound is based on a few studies in honey bees (Esch,1961; Wenner, 1962; Michelsen et al., 1986; Michelsen et al., 1987;Michelsen, 2003) and in bumble bees (Schneider, 1975). In honeybees, wing oscillations going along with the thoracic vibrationstransform these into airborne sound (Esch, 1961; Wenner, 1962;Michelsen et al., 1987). In bumble bees, on the other hand, wingoscillations are not significantly involved in the emission of airbornesound (Schneider, 1975). The defence sounds of bumble bee queens(sound pressure), which could be recorded behind, laterally and in

front of the bees, remained largely unaffected by the partial or eventhe complete ablation of the wings (Schneider, 1975).

The physical parameter of airborne sound relevant as input toJohnston’s organ in the pedicellus of the bees’ antenna, themechanoreceptor potentially involved in its perception, is air particlemovement (Dreller and Kirchner, 1993; Michelsen, 1993). Close tothe abdomen of dancing honey bees, strong air particle oscillationswith velocity amplitudes of up to 70·cm·s–1 (peak to peak, p-p) weremeasured. This value decreased rapidly with distance from the bee(Michelsen et al., 1987). In addition to these particle oscillations,honeybees generate a unidirectional ‘jet airflow’ during their dance,but only when the wingtips of the dancer are apart by more than7·mm (Michelsen, 2003). The study of a mechanical bee modelsuggested that this airflow, directed away from the abdomen, isformed by the air emanating from the space between the wings andthe abdomen. In contrast to the air particle oscillations, the amplitudeof the jet airflow decreased only slowly and linearly with distanceto the bee (Michelsen, 2003).

In stingless bees, nothing is known so far about the transformationof thoracic vibrations to airborne sound, even though airborne soundhas been considered important as a carrier of information (Esch,1967; Nieh, 1998; Nieh et al., 2003). In the present study, wetherefore asked the following questions. (1) How strong is theairborne sound (particle velocity and sound pressure) generated byvibrating stingless bees? (2) Is airborne sound limited to theabdominal region of the vibrating bee, as is the case in honey bees?(3) How important are the wings for the transformation of thorax

The Journal of Experimental Biology 211, 686-698Published by The Company of Biologists 2008doi:10.1242/jeb.013938

The sound field generated by tethered stingless bees (Melipona scutellaris):inferences on its potential as a recruitment mechanism inside the hive

Michael Hrncir1,2,*, Dirk Louis P. Schorkopf2, Veronika M. Schmidt2, Ronaldo Zucchi1 and Friedrich G. Barth2

1Department of Biology, University of São Paulo, FFCLRP, Av. Bandeirantes 3900, 14040-901 Ribeirão Preto, SP, Brazil and2Department of Neurobiology and Cognition Research, University of Vienna, Althanstrasse 14, A-1090 Vienna, Austria

*Author for correspondence (e-mail: [email protected])

Accepted 17 December 2007

SUMMARYIn stingless bees, recruitment of hive bees to food sources involves thoracic vibrations by foragers during trophallaxis. Thetemporal pattern of these vibrations correlates with the sugar concentration of the collected food. One possible pathway fortransfering such information to nestmates is through airborne sound. In the present study, we investigated the transformationof thoracic vibrations into air particle velocity, sound pressure, and jet airflows in the stingless bee Melipona scutellaris.Whereas particle velocity and sound pressure were found all around and above vibrating individuals, there was no evidence fora jet airflow as with honey bees. The largest particle velocities were measured 5·mm above the wings (16.0±4.8·mm·s–1). Arounda vibrating individual, we found maximum particle velocities of 8.6±3.0·mm·s–1 (horizontal particle velocity) in front of the beeʼshead and of 6.0±2.1·mm·s–1 (vertical particle velocity) behind its wings. Wing oscillations, which are mainly responsible for airparticle movements in honey bees, significantly contributed to vertically oriented particle oscillations only close to the abdomenin M. scutellaris (distances �5·mm). Almost 80% of the hive bees attending trophallactic food transfers stayed within a range of5·mm from the vibrating foragers. It remains to be shown, however, whether air particle velocity alone is strong enough to bedetected by Johnstonʼs organ of the bee antenna. Taking the physiological properties of the honey beeʼs Johnstonʼs organ asthe reference, M. scutellaris hive bees are able to detect the forager vibrations through particle movements at distances of up to2·cm.

Key words: stingless bees, thorax vibration, airborne sound, airflow, particle velocity, signal transmission, recruitment communication.

THE JOURNAL OF EXPERIMENTAL BIOLOGY

687Sound field generated by vibrating bees

vibrations to airborne sound? (4) Do vibrating stingless beesgenerate ‘jet airflows’ like honey bees? (5) Do hive bees stay closeenough to a forager to detect with their antennae the particle velocityresulting from the forager’s thoracic vibrations?

MATERIALS AND METHODSBees and study site

Stingless bees Melipona seminigra Friese 1903 generate pulsed‘annoyance buzzing’ when tethered with a sling around their neck(Hrncir et al., 2008). Although annoyance buzzing differedsignificantly with respect to both the main frequency componentand the velocity amplitude from forager vibrations, the mechanismof generation is similar in these two types of vibrations. Mostimportantly for their putative transformation into airborne sounds(Michelsen et al., 1987), both vibration types resulted in oscillationsof the wings to a similar degree (average velocity amplitudemeasured at the wingtips: annoyance buzzing, 688·mm·s–1; foragervibrations, 660·mm·s–1; average gain between thorax and wingtips:annoyance buzzing, 16.2·dB; forager vibrations, 17.9·dB) (Hrnciret al., 2008). The way that thoracic vibrations are transformed intoairborne sounds, therefore, is very similar in these two types ofvibrations. The study of annoyance buzzing has the great advantageover the study of forager vibrations that the first type of vibrationsis generated in a controllable environment and sensors can be easilypositioned around the bees. However, differences in the absolutevalues of particle velocity and sound pressure due to differences inthe velocity amplitude and the main frequency component betweenthe two vibration types must be taken into account.

In the present study we examined bees of the species Meliponascutellaris Latreille 1811, which are similar in size to M. seminigra,and reliably emit annoyance buzzing when sling-tethered as well(M.H., unpublished). Two colonies were housed in wooden nest-boxes inside a laboratory building on the campus of the Universityof São Paulo in Ribeirão Preto, Brazil. For video recordings oftrophallactic interactions between foragers and hive bees we installedan acrylic, glass-covered observation box (10�5�4·cm3) betweenthe nest and the entrance/exit tube through the wall. In most of thecases the returning foragers distributed their nectar or sugar wateramong nestmates inside this observation box (see Hrncir et al.,2004b; Hrncir et al., 2006b). The recordings described in the presentstudy were made between December 2005 and April 2006.

Sound field generated by vibrating beesWe measured the air particle velocity (amplitude p-p) and the soundpressure (pressure amplitude p-p) induced by the thoracic vibrationsof sling-tethered bees. Sound pressure is not of immediateimportance here because no pressure receivers are known in bees.Yet, sound pressure measurements enabled us to compare our resultswith those of the existing literature. Both air particle velocity andsound pressure were recorded using a MicroflownTM USP-probe(UT0406-5, Microflown Technologies, Arnhem, The Netherlands)which combines three particle velocity sensors (sensitivity:15·mV/[mm·s–1]) and a pressure microphone (sensitivity: 14mV/Pa). At frequencies relevant for the present study [mainfrequency range of stingless bee thorax vibrations: 200–600·Hz(Hrncir et al., 2006a)], particle velocities measured with the USP-probe showed an average deviation of 12.7% (range: 8–18%) fromparticle velocities measured under the same experimental conditionsin our Vienna laboratory by means of particle image velocimetry(DPIV system: 2 New wave Mercury Nd:YAG lasers and an IDTiNanoSense TR camera, Dantec Dynamics, Skorlunde, Denmark).Hence, an average measurement error of ±1.07·dB relative to the

DPIV measurements has to be taken into consideration for theparticle velocities recorded in the present study.

To record the sound field around sling-tethered individuals(Ntotal=47), bees were placed on a plane acrylic substrate(15�15·cm2). Particle velocity was measured both above andaround the vibrating bees (Fig.·1). The sensor positions were atdistances of 5, 10, 15 and 20·mm from the bee (Fig.·1). Due toslight, inevitable movements of the bees during the recordings,the accuracy of these measurement distances was ±1·mm. Abovethe bees (N=11), we measured the particle velocity orientedperpendicularly to the substrate above the head, above the thoraxand above the wings close to the wingtips (Fig.·1B, inset). In theplane around the bee (5·mm above the substrate), two componentsof particle velocity were investigated: (i) the particle velocityoriented perpendicularly to the substrate (vertically orientedparticle velocity; N=12), and (ii) the particle velocity orientedparallel to the substrate and towards/away from the vibrating bee(horizontally oriented particle velocity, N=12) (ii) (Fig.·1). Inaddition to the particle velocity caused by the vibrating bee itself,part of the vertically oriented particle velocity originated from

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Fig.·1. Airborne sound (sound pressure, mPa, and air particle velocity,mm·s–1) generated by sling-tethered stingless bees was measured using aMicroflownTM USP-probe. (A) We measured particle velocity in thehorizontal plane around the bee as well as above the vibrating individual. Inthe horizontal plane, the microphone to measure sound pressure and theairflow sensors (S) to measure air particle velocity either parallel to thesubstrate or perpendicular to it were kept at a constant distance of 5·mmabove the plane acrylic plate used as substrate (15�15·cm2). (B) Soundpressure and air particle velocity were picked up at 24 differentmeasurement points in the horizontal plane around the vibrating bee. Thedifferent directions of the measurement points relative to the long axis ofthe bee were labelled (i-vi). Inset: USP probe positions above the beeʼshead (He), thorax (Tx) and wingtips (Wt); only measurement points (filledcircles) at 5·mm distance are shown.


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sound reflected by the substrate. During foraging, collecting beesgenerate their thoracic vibrations predominantly close to the nestentrance on particular structures made of stiff batumen (Hrnciret al., 2006b; Morawetz, 2007; Morawetz et al., 2007). These oftentubular ‘entrance structures’ certainly also reflect the airbornesounds produced by foragers. Due to the irregular form of theentrance structures, however, and due to the variability in thematerials used, sound reflections in the natural situation areexpected to be more complex than those from the flat acrylicsurface used in the present study. Nevertheless, similarities in theway reflected sound effects the air particle velocity can beexpected between the natural situation and the situation used inthe present study. Assuming no differences between the soundfields on the left and right side of a bee, we measured on oneside only. Sound pressure was picked up in the horizontal planearound the bees (N=12) at the same measurement points as theparticle velocity (Fig.·1B). The sling-tethered bees showed slightintra-individual variations in the generation of thoracic vibrationsduring an experiment (average variation: velocity amplitude,±12.5%; main frequency component, ±3.7%; duration of singlepulses, ±12.5%; pulse sequence, ±14.1%). We therefore took themeasurements (12 different measurement points above the beesor 24 different measurement points in the horizontal plane aroundthe bees) in an arbitrary sequence to reduce any bias caused bypotential differences in signalling due to increasing exhaustionof the bees along with the duration of a recording. Sling-tetheredbees generated annoyance buzzing for about 10·min (Hrncir etal., 2008). In the present study, the recordings covered timeperiods between 3 and 5·min per investigated bee.

To judge the significance of the wings for the transformation ofthorax vibrations into particle velocity and sound pressure we clippedthe wings close to their base. Immediately after wing ablation, therespective aspect of the sound field was measured again with thesensor at the same positions as before. At all measurement points,the respective sound field was thus measured twice for each individual.

The closest possible distance between the USP-probe and thevibrating bee was 5·mm, which prevented the tethered individualsfrom getting hold of the sensors and damaging them. The amplitudesof air particle velocity at still closer distances (1, 2, 3 and 4·mm)were extrapolated using a hyperbolic decay function (Regressionwizard, SigmaPlot 2001, SPSS Inc., Chicago, IL, USA; seeAppendix·1). Extrapolations were only applied to particle velocitiesbecause sound pressure is not immediately relevant for any knownsensory organ of bees.

Preservation of signal patternIn order to see the extent to which the temporal pattern of the pulsedthorax vibrations is preserved in airborne signals, we simultaneouslyrecorded the thorax vibrations and the particle velocity generated bysling-tethered bees (N=12 bees). Thorax vibrations were recorded asvelocities using a portable Laser Doppler Vibrometer (PDV-100,Polytec, Waldbronn, Germany). The measurement point of the laservibrometer was on the bee’s scutum. The particle velocity wasmeasured at 5·mm and 10·mm behind the vibrating bee, lateral to itsthorax and in front of its head. The following parameters wereanalysed: the duration of single pulses (PD), their main frequencycomponent (MF), and the pulse sequence (PS), which is the time fromthe onset of one pulse to the onset of the following pulse (Fig.·2).

Jet airflowTo investigate the potential existence of a unidirectional (jet)airflow generated by vibrating bees, we positioned a custom-

M. Hrncir and others

made hot-wire anemometer sensitive to low frequencies(~1.2mV/[mm·s–1]) 5·mm behind a total of six sling-tethered bees(where the jet should occur), and 5·mm laterally of its thorax (wherethe jet seemed unlikely). Simultaneously, the thorax vibrations ofthe bees were picked up with a laser vibrometer. The anemometerwas placed both behind the bee and laterally to it, for about oneminute each. We reduced the influence of ambient air currents withinthe laboratory by performing the measurements inside a cardboardarena (20�20�10·cm2). However, sound reflections from thecardboard box, air currents caused by the cooling systems of ourequipment (laser vibrometer, notebook), and electrical noiseoriginating from the current supply could not be fully avoided andresulted in background noise equivalent to about 2·mm·s–1. Yet, jetairflows if present should still have been detected, as they werereported to reach velocity amplitudes of 150·mm·s–1 at a distanceof 5·mm behind vibrating honey bees (Michelsen, 2003).

Distribution of hive bees around vibrating foragersTo see whether hive bees stay within a range around vibratingforagers allowing signal transmission through airborne sound, wevideotaped 20 trophallactic interactions of six different foragers(digital video-camera: Panasonic, NV-GS400GE; 30·frames·s–1). Forthese recordings, the foragers (one individual per recording day)had been trained to collect sugar solution (50% cane sugar w/w) atan artificial food source 15·m away from the nest entrance. Thevideo-caption showed the vibrating forager and a ca. 2·cm rangearound it during trophallaxis. This caption size allowed both a good

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Fig.·2. Simultaneously measured thorax vibrations (laser vibrometer) andair particle velocity (USP-probe). In the case shown here, the USP-probewas 5·mm away from the bee at direction iii (see Fig.·1). (A) Velocityamplitude (VA), pulse duration (PD), and pulse sequence (PS). (B) A singlepulse illustrating the close similarity between the thorax vibrations and theair particle oscillations. (C) Frequency power spectra of the pulses shownin B; MF, main frequency component.



view of the distribution of the hive bees around the forager, andexact distance measurements. The recordings were analysed usingthe software VideoPoint 2.5 (Lenox Softworks Inc., Lenox, MA,USA). Due to their movement and the resulting blurred video-image,it was impossible to identify the exact position of the antennae.Instead, we took the midpoint of the hive bees’ heads as a referenceto measure their position. We analysed the closest distance to thevibrating forager for those hive bees that were not involved in thefood transfer during the respective trophallactic interaction. We onlytook those hive bees into account that ‘showed an interest’ in theforager without getting involved into trophallactic food transfer. Asa measure for ‘being interested’ we took the approach towards theforager in a roughly straight line. Several hive bees that just passedby, moved out of the caption, or did not clearly change positionduring the recording were excluded from the analysis. Because thecaption size of the camera had a radius of only about 2·cm, we couldnot determine at which points the bees decided to move towardsthe forager. However, our emphasis was to determine whether thosehive bees that moved towards the forager do get close enough tothe vibrating bee to detect any particle velocity generated by itsthoracic vibrations.

Analysis and statisticsThe output signals of the USP-probe, the hot-wire anemometer andthe laser vibrometer were fed into a notebook (Pentium IV, 2.4·GHz)using a 24-bit stereo soundcard (PSC 805, Philips, Amsterdam, TheNetherlands) and the software Soundforge 7.0 (Sony Digital Inc.,Madison, WI, USA) at a sampling rate of 44.1·kHz. For the analysisof thorax vibrations and airborne sound we used the softwaresSpectraPro 3.32 (Sound Technology Inc., Campbell, CA, USA),SigmaPlot 2001 (SPSS Inc., Chicago, IL, USA) and SigmaStat 3.10(Systat Software Inc., San Jose, CA, USA).

For each individual, the mean values of sound pressure or airparticle velocity at each measurement point were calculated from15–30 vibratory pulses. The statistical tests were performed withthese representative mean values. Because the data were normallydistributed in all cases (Kolmogorov–Smirnov test, P>0.05) andshowed equal variance (Levene median test, P>0.05), we appliedparametric tests. The Paired t-test was used to compare theamplitudes of airborne sounds at each measurement point beforeand after clipping the wings. One-way repeated-measures ANOVA(post-hoc pairwise comparison: Tukey test) indicated possiblesignificant differences between amplitudes measured at the samedistance but in different horizontal directions to the vibrating bee.Spearman rank correlation was applied to test the relationshipbetween signal parameters (PD, pulse duration; PS, pulse sequence;MF, main frequency component; VA, velocity amplitude) of thoraxvibrations and air particle oscillations. The correlation coefficient(rS) indicates the degree of association between them (rS=1, highassociation; rS=0, no association). Throughout the text, values arepresented as mean ±1 s.d. N refers to the number of differentindividuals tested, and n to the number of single pulses evaluated.The level of significance of differences was taken as P�0.05. ABonferroni correction for the level of significance was performed(Pcorr.�0.05/number of comparisons) (Sokal and Rohlf, 1995) whendata sets were used for more than one statistical comparison.

RESULTSSound field generated by vibrating bees

Particle velocityDuring annoyance buzzing, air particle velocities could berecorded at all measurement points both above and in the

horizontal plane around a vibrating bee (Figs·3–6). There weresignificant differences between the amplitudes picked up at thesame distance but in different directions from the vibratingindividual (one-way repeated-measures ANOVA: Pcorr.�0.025;Tables·1, 2). The highest particle velocity was measured 5·mmabove the plane of the wings (16.0±4.76·mm·s–1). Here, thevelocity amplitude of the air particle oscillations was significantlylarger than the highest values measured in the horizontal plane

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Fig.·3. Typical examples of airborne sound picked up with the USP-probe5·mm in front of the head (left panels) and 5·mm behind thewingtips/abdomen (right panels). (A) horizontally and (B) vertically orientedair particle oscillations, and (C) sound pressure induced by the thoraxvibrations before (upper rows) and after wing ablation (lower rows).


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around the bee (vertically oriented oscillations, 5·mm behind thewingtips: 6.0±2.08·mm·s–1; horizontally oriented oscillations,5·mm in front of the head: 8.6±2.95·mm·s–1; one-way ANOVA,F2,32=26.60, P<0.001) (compare Table·1 with Table·2). Above thebee, the vertically oriented particle velocity steadily decreasedbetween the measurement points above the wings and themeasurement points above the head (Fig.·4, Table·1). In the planearound the bee, vertically oriented particle velocity was strongestbehind the bee’s wingtips and weakest in front of its head atdistances �5·mm (values extrapolated from the exponentialdecay functions given in Appendix·2) (Fig.·5, Table·2). Atdistances beyond 5·mm, the field of vertical particle velocitieswas largely homogeneous around the vibrating bee (one-wayrepeated measures ANOVA: no significant differences betweendirections; Fig.·5, Table·2). Horizontally oriented particle velocity


around the bee was largest in front of the bee’s head, and lowestlateral to the bee’s thorax at distances �5·mm (Fig.·6, Table·2).Closer to the vibrating bee, at distances <5·mm (valuesextrapolated from the exponential decay functions given inAppendix·2), the field of horizontally oriented particle oscillationswas highly polarised, showing highest velocity amplitudes in frontof the bee’s head and lowest values behind its wings (directionv; Fig.·6, Table·2). Thus, the polarization of the field ofhorizontally oriented particle velocity decreased with increasingdistance to the vibrating bee, becoming insignificant (P>0.05) ata distance of 20·mm.

Sound pressureSimilar to horizontally oriented particle velocity, sound pressure

in the plane around the bee was generally highest in front of thebee’s head and lowest behind its wingtips (directions v and vi)(Fig.·7, Table·3). The highest sound pressure recorded was at 5·mmin front of the bee’s head (323.0±85.6·mPa). Differences betweenthe fields of sound pressure and horizontally oriented particlevelocity (compare Table·2 with Table·3; e.g. at a distance of 15·mmto the vibrating bee, the highest sound pressure was recorded laterallyof the bee’s thorax, and the highest horizontal particle velocity infront of its head) might originate from slight differences in thedistance between the vibrating bee and the sensor between differentrecordings (±1·mm accuracy: see Materials and methods).Alternatively, or in addition, they point to the fact that close to avibrating bee sound pressure and particle velocity might not berelated to each other in a simple way.

The significance of the wings for the generation of the soundfield

By removing the bee’s wings, we determined their significance forthe transformation of thorax vibrations into airborne sounds.According to a comparison of air particle velocity and sound pressurebefore and after wing removal neither the amplitude of the horizontally

Table 1. Mean values of vertically oriented air particle velocityabove the head, the thorax and the wings close to the wingtips

Distance Particle velocity (mm·s–1)

(mm) Head Thorax Wingtips F2,30 P

1* 23.54 43.15 61.46 – –2* 12.55 22.39 31.62 – –3* 8.56 15.11 21.29 – –4* 6.49 11.41 16.05 – –5 5.66a 10.91b 16.03c 24.45 <0.00110 2.05a 3.04b 3.58b 14.29 <0.00115 1.47a 1.62a,b 1.72b 5.20 0.01520 1.27 1.43 1.37 2.24 0.13 n.s.

Bold letters emphasize highest values at the given distance. Air particle velocities measured at same distances (�5·mm) but at different

positions were compared using one-way repeated measures ANOVA (F-values given). Level for significance of difference is Pcorr.�0.025. Values ina row that have same superscript letters did not differ significantly fromeach other (pairwise comparison: Tukey-test, P>0.05); n.s., not significant.

*Values extrapolated from hyperbolic decay function (see Appendix·2).

Table 2. Mean values of both vertically and horizontally oriented air particle velocities (p-p) around a vibrating bee, at different distances anddirections (i–vi) relative to the vibrating bee

Distance Particle velocity (mm·s–1) in directions i–vi

(mm) (i) (ii) (iii) (iv) (v) (vi) F5,55 P

Vertically oriented 1* 7.78 11.98 21.41 17.52 18.48 25.47 – –2* 5.65 7.53 11.06 10.09 10.18 13.25 – –3* 4.57 5.49 7.46 7.09 7.02 8.95 – –4* 3.84 4.32 5.63 5.46 5.36 6.76 – –5 3.31a 3.58a,b 4.72b,c 4.86c,d 4.67b,c 6.03d 11.70 <0.001

10 2.00 1.82 2.00 2.02 1.93 2.02 0.74 0.60 n.s.15 1.33 1.26 1.41 1.26 1.29 1.33 1.62 0.17 n.s.20 1.11 1.11 1.04 1.16 1.07 1.13 1.43 0.23 n.s.

Horizontally oriented 1* 20.84 10.86 9.92 10.68 9.66 10.88 – –2* 16.22 9.15 8.27 8.90 8.21 9.17 – –3* 12.87 7.78 6.96 7.50 7.03 7.79 – –4* 10.39 6.67 5.92 6.37 6.07 6.68 – –5 8.57a 5.82b 5.16b 5.53b 5.34b 5.83b 11.17 <0.00110 3.34a 2.82a,b 2.31b 2.57b 2.64a,b 2.83a,b 4.17 0.00315 1.98a 1.76a,b 1.48c 1.54b,c 1.70b,c 1.76a,b 7.85 <0.00120 1.55 1.44 1.35 1.41 1.36 1.43 1.76 0.14 n.s.

See Fig.·1B for details on directions i–vi. Bold letters emphasize highest values measured at the given distance. Particle velocities measured at the same distances (�5·mm) but in different directions were compared using one-way repeated measures ANOVA (F-values

given). Level for significance of difference: Pcorr.�0.025. Values in a row that have same superscript letters did not differ significantly from each other(pairwise comparison: Tukey-test, P>0.05); n.s., not significant.

*Values extrapolated from hyperbolic decay function (see Appendix·2).



oriented particle velocity nor the sound pressure were significantlyinfluenced (paired t-test: Pcorr.>0.025; Figs·6 and 7). Yet, removingthe wings reduced the amplitude of vertically oriented particlevelocity above and behind the abdomen. However, this effect wasstatistically significant only at a distance of 5·mm from the vibratingindividuals (paired t-test: Pcorr.<0.025; Figs·4 and 5).

To determine which portion of the particle velocity is generatedsolely by the oscillating wings, we subtracted each bee’s meanparticle velocity generated after wing removal from its ‘intact’ value.Again, an exponential decay function was applied to extrapolateparticle velocity values close to the bees. As shown in Figs·4 and5, the significance of the wings for vertical particle oscillations(above and around a bee) was restricted to the immediateneighbourhood of the wings, and the abdomen, respectively. Theoscillating wings were responsible for a part of the horizontal particleoscillations measured laterally to the bee and in front of it (Fig.·6).Compared to the effect on vertically oriented particle oscillations,however, this effect was very small.

Preservation of temporal signal patternsAccording to previous studies (Hrncir et al., 2006a), the potentialsignal value of air movement (sound) should depend on the extentto which the temporal pattern of the thorax vibrations is preservedafter its transformation into particle velocity. At all measurementpoints around a vibrating bee (directions i, iii and vi, at both 5 andat 10·mm distance from the individual) the temporal pattern of theair particle oscillations highly correlated with that of the thoraxvibrations (5·mm, Spearman rank correlation, i: rS,PD=0.96,

rS,PS=1.00, rS,MF=0.98, N=12, n=156; iii: rS,PD=0.97, rS,PS=1.00,rS,MF=0.98, N=12, n=155; vi: rS,PD=0.96, rS,PS=1.00, rS,MF=0.91;N=12, n=183; 10·mm, Spearman rank correlation, i: rS,PD=0.96,rS,PS=1.00, rS,MF=0.94, N=12, n=142; iii: rS,PD=0.93, rS,PS=1.00,rS,MF=0.95, N=12, n=153; vi: rS,PD=0.95, rS,PS=1.00, rS,MF=0.96;N=12, n=152).

Vibrating stingless bees do not generate jet airflowsThe possible existence of jet airflows generated by vibratingstingless bees was tested by measuring the air particle movementbehind the wingtips (direction vi) and laterally of the thorax(direction iii) at a distance of 5·mm. In honey bees, the wingmovements going along with the thorax vibrations during thewaggle dance were found responsible for the generation of anair jet with velocity amplitudes of up to 150·mm·s–1 behind thewingtips (Michelsen, 2003). In M. scutellaris, no obviousdifferences existed between the position behind the vibratingbee and the lateral position (Fig.·8). Despite the strongbackground noise in our recordings (Fig.·8), a strong,unidirectional jet airflow would have been detected if present.However, the recordings made behind and laterally to the beesdid not differ.

Distribution of hive bees around vibrating foragersDuring 20 trophallactic interactions, we determined the closestdistance between 128 hive bees and the vibrating foragers (N=6).In 77.3% of the observed cases (99 individuals), the heads of thehive bees were closer than 5·mm to the forager, and in only 3.1%

20

15

10

5

0

Head Thorax Wingtips/abdomen

s–1)

mm(

edutilpma

yticoleV

A

5 10 15 20 5 10 15 20Distance (mm)

5 10 15 20

*

C DB

40

10

2mm s–1

5 mm

Fig.·4. Vertically oriented air particle velocity amplitude VA (p-p) above a vibrating bee. (A) Mean values ±1 s.d. (N=11) above head, thorax andwingtips/abdomen, before (filled circles) and after wing removal (open circles). Circles are slightly displaced horizontally for better visibility. Asterisk indicatessignificant difference (paired t-test; Pcorr.�0.025) between intact and wingless bees. (B–D) Ranges above the vibrating bee in which air particle velocities hadthe same mean amplitudes (extrapolated from hyperbolic decay functions, see Appendix 2). Different colours indicate mean velocity amplitudes between2·mm·s–1 and 40·mm·s–1 as explained by the logarithmic colour scale. (B) Intact individuals, (C) wingless individuals, (D) portion of particle velocitygenerated solely by wings (see text for details). Values for directions in front and behind of the bee were taken from vertically oriented particle oscillations inFig.·7. Shaded area above bee marks the 1·mm range that cannot be accurately described by decay functions (see Appendix·1). Because the airflowsensors were positioned at least 5·mm above the substrate, no values are given for the region below 5·mm (shaded area).


692

of the cases (4 individuals), the bees stopped moving towards theforager at distances larger than 10·mm (Fig.·9). The majority of thehive bees (76.6%, 98 individuals) took a position lateral to theforagers. The antennal tips of all bees less than 5·mm away fromthe forager were certainly able to touch the forager’s body (Fig.·9A).According to observations without video-equipment (D.L.P.,unpublished), hive bees indeed do touch a vibrating forager’s bodywith their antennae.

DISCUSSIONGeneration of airborne sound

In bees there seem to be at least two different ways to transformthorax vibrations into airborne sounds. Whereas in honey bees thewings are important for this transformation, in stingless bees andbumble bees (Schneider, 1975) the structure responsible for thegeneration of airborne sounds is predominantly the vibrating thoraxitself.

A simple comparison of the distribution of sound pressuresproduced by a vibrating stingless bee (M. scutellaris) and a honeybee (Apis mellifera), already suggests a difference in the respectivegeneration of the sound fields. In the dancing honey bee, soundpressure was as high as P=156·mPa 10·mm behind its abdomen,and as high as P=127·mPa lateral to its wings (Esch, 1961). Nosounds could be heard in recordings made in front of the head, whichwas taken to indicate that airborne sounds are generated by theoscillating wings (Esch, 1961; Wenner, 1962). This is supported by


findings of Michelsen et al. (Michelsen et al., 1987). After removingthe wings from one body side, the sound pressure measured laterallyon the winged side was 3–4 times higher than that on the winglessside. With all four wings removed, the amplitude of the sounddecreased to values below the sensitivity of the pressure microphonelocated 2·mm above the bee’s abdomen (Michelsen et al., 1987).

In M. scutellaris, the sound pressure behind the wingtips ofvibrating sling-tethered individuals was very similar to that measuredin honey bees (direction vi, 10·mm distance to wingtips: P=151·mPa,Table·3). However, different from honey bees, sound pressure couldbe measured all around an individual and even reached its maximumin front of its heads (Fig.·7, Table·3). Clipping the wings did notaffect sound pressure (Fig.·7). Apparently, in M. scutellaris the wingsdo not play a significant role in the transformation of thoracicvibrations into sound pressure. Similarly, in bumble bee queensemitting a pulsed defence buzzing when tethered (Schneider, 1975),sound pressure could be recorded behind, laterally and in front ofthe vibrating individuals. Unfortunately, sound pressure values forthe different positions around the bee are not provided in thispublication (Schneider, 1975). However, similar to our findings, thesound pressure did not change in general in amplitude followingthe removal of the wings (Schneider, 1975).

Air particle movementThe physical parameter most relevant for the sensory perception ofairborne sound by bees is air particle movement. In dancing honey

0

3

6

9(i) (ii) (iii) (iv) (v) (vi)

5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20Distance (mm)

A

**

B DC

40

10

2mm s–1

5 mm

s–1)

mm(

edutilpma

yticoleV

Fig.·5. Vertically oriented air particle velocity amplitude VA (p-p) around a vibrating bee. (A) Mean values ±1 s.d. (N=12) picked up 5, 10, 15 and 20·mm fromthe vibrating bees and at measurement points in different directions relative to the long axis of the bee (i–vi; see Fig.·1B); values before (filled circles) andafter wing removal (open circles). Circles are slightly displaced horizontally for better visibility. Asterisks indicate significant difference (paired t-test;Pcorr.�0.025) between intact and wingless bees. (B–D) Ranges around the vibrating bee with particle velocities of the same mean amplitudes (extrapolatedfrom hyperbolic decay functions, see Appendix 2). Colour scale as in Fig.·4. (B) Intact individuals, (C) wingless individuals, (D) particle velocity generated onlyby wings (see text for details). Shaded area around bee: marks the 1·mm range that cannot be accurately described by decay functions (see Appendix 1).



bees, two different forms of air particle movement have beendescribed. First, the oscillating wings create intense air particleoscillations close to their edges (Michelsen et al., 1987). Second,air that moves out from the space between the wings and theabdomen during wing vibrations creates an air jet moving awayfrom the bee’s abdomen (Michelsen, 2003). Both these forms of airparticle movement in the honey bee depend on the wing oscillationsthat go along with the thoracic vibrations. In M. scutellaris, particlevelocity, similar to sound pressure, was predominantly generatedby the thoracic oscillations. As expected, oscillations of the wingssignificantly affected the vertically oriented particle velocity closeto the abdomen only (Figs·4–6).

The differing importance of the wings for the generation of thesound field in A. mellifera and M. scutellaris, respectively, is thoughtto be due to a difference in wing position. Whereas honey beesgenerate sounds with splayed wings during their dance movements,with the wing tips 5–9·mm apart (Michelsen, 2003), stingless beesgenerate thorax vibrations during both forager vibrations andannoyance buzzing with their wings closely folded over the abdomen(Lindauer and Kerr, 1958; Hrncir et al., 2006a; Hrncir et al., 2006b;Hrncir et al., 2008). Due to the folding of the wings, these areuncoupled from the indirect flight mechanism and, thus, theiroscillation amplitude during ‘buzzing’ is strongly reduced comparedto that during flight (Heinrich, 1993; King et al., 1996). A spreadingof the wings increases the effective wing area (Schneider, 1975)

which, in turn, increases the amount of air between the wings andthe abdomen which is moved by every wing stroke. Wing positionprobably also influences the way how the air is expelled from thisspace as indicated by the observation that the splaying of the wingsis essential for the generation of the honey bee’s jet airflow. Aunidirectional airflow behind a dancing honey bee could only bemeasured when the dancer’s wingtips had a distance of at least2.5·mm from each other (Michelsen, 2003). In accordance with this,no jet airflow could be measured behind vibrating M. scutellaris(Fig.·8), which generates sound with its wings completely foldedover the abdomen.

Use of airborne sounds for information transferIn Melipona bees, the temporal pattern of the forager’s thoracicvibrations predominantly depends on the sugar concentration of thecollected food (Hrncir et al., 2006a). The airborne sound going alongwith the thoracic vibrations was repeatedly assumed to transmitinformation to the nestmates although particle velocity had not beenmeasured in these studies (Esch, 1967; Nieh et al., 2003). Whereasthe temporal pattern of the thorax vibrations (pulse duration, pulsesequence and main frequency component) is indeed well preservedin the airborne sounds [sound pressure (Hrncir et al., 2004a); airparticle oscillations, present study] the crucial question whether theair particle velocity close to a vibrating bee is strong enough to bedetected by the hive bees is still not answered yet.

12

9

6

3

0

(i) (ii) (iii) (iv) (v) (vi)

A

5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20Distance (mm)

B C D

40

10

2mm s–1

5 mm

s–1)

mm(

edutilpma

yticoleV

Fig.·6. Horizontally oriented particle velocity amplitude VA (p-p) around a vibrating bee. (A) Mean values ±1 s.d. (N=12) at distances of 5, 10, 15 and 20·mmfrom the vibrating bees at measurement points in different directions relative to the long axis of the bee (i–vi; see Fig.·1B); values before (filled circles) andafter wing removal (open circles). Circles are slightly displaced horizontally for better visibility. There were no significant changes of values after wingablation (paired t-test; P>Pcorr, 0.025). (B–D) Ranges around the vibrating bee where particle velocities had the same mean amplitudes (extrapolated fromhyperbolic decay functions, see Appendix 2). Colour scale as in Fig.·4. (B) Intact individuals, (C) wingless individuals, (D) portion of particle velocitygenerated solely by wings (see text for details). Shaded area around bee marks the 1·mm range that cannot be accurately described by decay functions(see Appendix·1).


694

The candidate mechanosensory organ able to detect particlevelocity is Johnston’s organ in the antennal pedicel, which isstimulated by the deflection of the flagellum (Snodgrass, 1956;Heran, 1959; Tsujiuchi et al., 2007). To date, neither thephysiological nor the mechanical properties of this mechanoreceptorare known in stingless bees. A comparison with data available forthe honey bee may be helpful, nevertheless. It has only recentlybeen demonstrated (Tsujiuchi et al., 2007) that the minimumdisplacement amplitude of the honey bee’s flagellar tip necessaryto elicit a neural response of Johnston’s organ is 20·nm, achieved


by a free-field air particle displacement of 60·nm. The magnitudeof the sound-evoked compound potentials of Johnston’s organlinearly increased with antennal tip displacements up to 100·nm. Ata flagellar tip displacement above 200·nm, corresponding to a free-field air particle displacement amplitude larger than 5·�m, themagnitude of the neural response reached a saturation level(Tsujiuchi et al., 2007).

Adopting these findings for the recruitment communication ofM. scutellaris, we conclude that stingless bees in the nest shouldbe able to detect the particle velocities generated by foragers withtheir antennal mechanoreceptors. Taking the honey bee values, theminimum free-field particle velocities that can be detected by thebees are between 0.13·mm·s–1 at a frequency of 350·Hz and0.21·mm·s–1 at 550·Hz [frequency range of M. scutellaris foragervibrations (Hrncir et al., 2000)], corresponding to a particledisplacement of 60·nm (free-field) at these frequencies. Saturationof Johnston’s organ is reached at free-field particle velocitiesbetween 11.0·mm·s–1 (350·Hz) and 17.2·mm·s–1 (550·Hz),corresponding to a particle displacement of 5·�m at thesefrequencies.

Due to the difficulties in accurately positioning sensors aroundvibrating foragers during their trophallactic interactions with hivebees, it is an almost impossible task to properly measure particlevelocities induced by forager vibrations close to the receiver bee.Forager vibrations, however, are very similar in terms of themechanism of their generation to annoyance buzzing. Both typesof thoracic vibrations result to a similar degree in oscillations of thelegs and of the wingtips (Hrncir et al., 2008). Therefore, the studyof annoyance buzzing can give an insight into signals generatedduring forager vibrations. Yet, the velocity amplitudes of thoracicvibrations by foragers are about 55% of those during annoyancebuzzing (Hrncir et al., 2008). Since the particle velocity dependson the velocity amplitude of the sound source (Appendix·1), wemust take into account that the particle velocities generated byvibrating foragers might be only about half of the values recordedin the present study. Even so, and despite the complexities of thephysics of sound generation close to a structure like a vibratingthorax, hive bees of M. scutellaris should be able to detect foragergenerated particle velocities within a range of at least 2·cm fromthe vibrating bee (smallest measured particle velocity at 2·cm froma sling-tethered bee: 1.04·mm·s–1 r 0.52·mm·s–1 induced throughforager vibrations). At distances smaller than 5·mm from thevibrating bee, the particle velocity generated by foragers will evenresult in the maximum response of Johnston’s organ neurons. Themaximum particle velocities found in the present study were25.5·mm·s–1 (first standard deviation: ±8.7·mm·s–1) at 1·mm behind

the vibrating bee (r12.8·mm·s–1 in behindthe forager), 43.2·mm·s–1 (±15.6·mm·s–1) at1·mm above the thorax (r21.6·mm·s–1

above the forager’s thorax), and 61.5·mm/s(±18.5·mm·s–1) at 1·mm above the wings(r30.8·mm·s–1 above the forager’s wings).Hive bees that attended trophallactic eventsstayed predominantly within <5·mm fromthe vibrating forager (Fig.·9) and theirsplayed antennae were close to or indeedtouching the forager (Fig.·9A). Similarly, inM. panamica the antennal tips of hive beeswere within a distance of at most 2·mm fromthe vibrating forager’s body duringtrophallaxis, and in about 30% of the casesthe antennal tips were above the wings or

500

400

300

200

100

0

500

400

300

200

100

0

)aP

m(erusserp

dnuoS

500

400

300

200

100

05 10 15 20

Distance (mm)

5 10 15 20

ii

i

iviii

v

iv

Fig.·7. Sound pressure (p-p) around a vibrating bee. (A) Mean values ±1s.d. (N=12) measured at distances of 5, 10, 15 and 20·mm from thevibrating bees and at measurement points in different directions relative tothe long axis of the bee (i–vi; see Fig.·1B); values before (filled circles) andafter wing removal (open circles). Circles are slightly displaced horizontallyfor better visibility. Sound pressures generated by a bee before and afterwing removal do not differ significantly between intact and wingless bees(paired t-test; P>Pcorr, 0.025).

Table·3. Mean values of sound pressure (p-p) measured at the given distances anddirections (i–vi) relative to the vibrating bee

Distance Sound pressure (mPa) in directions i–vi

(mm) (i) (ii) (iii) (iv) (v) (vi) F5,55 P

5 323.0a 267.4a,b 302.7a,b 246.7b,c 215.8c 236.0b,c 6.25 <0.00110 207.1a 190.6a,b 199.1a 189.1a,b 180.2a,b 151.0b 3.49 0.00815 152.0a,b 169.6a 169.9a 154.8a,b 120.9b 124.2b 6.51 <0.00120 146.2a 135.6a 142.2a 127.7a,b 106.4b,c 97.5c 8.94 <0.001

See Fig.·1B for details on directions i–iv.Bold letters emphasize highest measured values at the given distance. Sound pressures measured at same distances (�5·mm) but in different directions were compared

using one-way repeated measures ANOVA (F-values given). Level for significance of difference isPcorr.�0.025. Values in a row that have same superscript letters did not differ significantly from eachother (pairwise comparison: Tukey-test, P>0.05).



the thorax of the forager (Nieh, 1998). In the case of physical contactbetween the hive bees’ antennae and the body of a forager, thethoracic vibrations will be directly transmitted. The thoracicvibrations will then be a stronger stimulus for Johnston’s organ thanthe air particle velocity around the bees (see Appendix 1).

In addition to using the temporal pattern of the airborne sounds(which highly correlates with the temporal pattern of the forager’sthoracic vibrations) as information on the profitability of the foodsource (Hrncir et al., 2004a), hive bees could use any air particlemovements to detect an active forager in the darkness of the hive.This information is important for both nectar processing bees andinactive foragers (Biesmeijer et al., 1998; Anderson and Ratnieks,1999). Thus, airborne sound may transmit different kinds ofinformation. Electrophysiological studies of the responses of theappropriate mechanoreceptors in stingless bees are needed to answerthis question.

APPENDIX 1Particle velocity radiated from spherical sound sources

Due to its complex oscillation movements, which are a result of theinterplay between different parts of the cuticle and the thoracicmuscles, not to mention the effects of oscillating wings and the head,

the bee’s thorax is far from representing a simple sound source.Nevertheless, calculations of sound radiated by theoretical soundsources (Morse, 1981; Jacobsen et al., 2007) might help to get morequantitative understanding of the air particle velocities very closeto the bees, where measurements were not possible. The modelsthat come closest to a vibrating thorax are a monopole (pulsatingsphere), and a dipole (sphere vibrating along polar axis).

Radiation of sound from monopole sourcesThe simplest sort of outgoing sound wave is from a uniformly

expanding and contracting sphere of radius a. The particle velocityu at distance r from the center of the sphere (r=a+d) at the frequencyv is (Jacobsen et al., 2007):

(Q(v), source strength; k(v)=2�v/c; r, distance from the center of thesphere; u, air particle velocity; v, oscillation frequency).

Knowing the velocity amplitude at the surface of the sphere (r=a)for a given frequency (U0(v)), we can determine Q(v):

(a, radius of the sphere; U0, velocity amplitude at the surface of thesphere).

Q(v) = , (A2) 4�a2U0(v)

k(v)a2+12

Q(v)

4� �ur(v)� = ,

r2(A1)

k(v)r2+12

100

0

–100

100

0

–100 0.5 s

vi

0.5 s

iii noitarbivxaroh

Twolfri

A

0.05 s

5

0

–5 0.05 s

Vel

ocity

(m

m s

–1)

Vel

ocity

(m

m s

–1)

vi

5 mm

iii

Fig.·8. Simultaneously measured thorax vibrations and unidirectional airmovements. A jet airflow was only to be expected behind the vibratingbees (see text). The airflow recordings made 5·mm behind the wingtips(direction vi relative to the long axis of the bee, see Fig.·1), and thosemade 5·mm laterally (direction iii relative to the long axis of the bee; seeFig.·1) did not differ. Scaling for the airflow was chosen in accordance withthe velocity amplitude of the air jet described in honey bees, 150·mm·s–1

(Michelsen, 2003). Insets: amplified vibratory pulses showing air particleoscillations along with the thorax vibrations.

100

80

60

40

20

05 10 15 200

)%(

seebevihfo

noitroporP

Distance to forager (mm)

HH

R

HM:otoh

PH

M:otohP

5 mm

A

B C

10 mm

(i)

(vi)

(iv)

(v)

(ii)

(iii)

Fig.·9. Distribution of hive bees (H) around a vibrating forager (F) duringtrophallactic food transfer measured within a circle of 2·cm radius aroundthe centre of the foragerʼs thorax. Food receivers (R) were not included inthe analysis. The closest position between the heads of hive bees(midpoint indicated by white dot) and the foragers served as a measure forthe distance. (B,C) Distribution of 128 hive bees attending 20 trophallacticinteractions (six different foragers). Different colours represent differentregions around vibrating foragers; the borderlines between different regionscorrespond to directions (i–vi) given in Fig.·1B.


696

From the combination of the Eqn·A1 and A2 results:

For the radiation of sound from the bee’s thorax considered a spherewith monopole character, Eqn·A3 can be transformed to:

(a, radius of the thorax; d, distance from the thorax; VAd, peak topeak air particle velocity at distance, d; VATx, velocity amplitudep-p of thoracic vibrations; k(MF)=2�MF/c; MF, main frequencycomponent).

Because:

Eqn·A4 can be simplified as:

Radiation from dipole sourcesIf the center of a sphere oscillated along the polar axis with avelocity of U0e–2�ivt, the radial velocity of the surface of the sphereis U0cos�e–2�ivt, where � is the angle from the polar axis. Closeto the source, if rr0, the particle velocity u at the distance r fromthe center of the sphere (r=a+d) at the frequency v is (Morse,1981):

(c, wave velocity; e, Euler’s number; K, constant; t, time; �, anglefrom the polar axis; �, density of air).

If the radius (a) of the sphere is small compared to the wavelength(which is the case with the thorax of bees), the constant K(v) can beapproximated as (Morse, 1981):

The radial velocity u(v) at r=a (the surface of the sphere) is (Morse,1981):

�u(v)� = U0(v)cos�e–2�ivt·. (A9)

Considering the thorax as sphere, and the radial velocity u(v) at itssurface as VATx, the peak to peak particle velocity VAd at distanced from the surface of the sphere can be estimated through acombination of Eqn·A7–A9:

Comparison between calculated and measured particlevelocity

For calculations of the particle velocity radiated from monopole(Eqn·A6) and dipole sources (Eqn·A10), the radius of the soundsource, its vibration velocity, and the main frequency component

(a+d)

a �

k(MF)a2+1(A5)

k(MF)(a+d)2+12

2,

VATxa2

(a+d)2 VAd =

k(MF)a2+1(A4)

k(MF)(a+d)2+12

2,

�ur(v)� = .r2

(A3) k(v)r2+12U0(v)a2

k(v)a2+12

⎛⎜⎝

⎞⎟⎠

4�3�v3a3U0(v)

c2K(v) � (A8) .

⎛⎜⎝

⎞⎟⎠

2K(v)

�c

⎛⎜⎝

⎞⎟⎠

1

k(v)r �ur(v)� = (A7) cos�e–2�ivt ,

3

VATxa

(a+d) VAd = (A6) .

VATxa3

(a+d)3 VAd = (A10) .


of the vibrations are required. From the laser-vibrometer recordingsin M. scutellaris, we can determine these two vibration parametersonly for the dorsal surface of the thoracic scutum. We assumed thethorax of the bee to be a sphere with the radius a=1.7·mm (mean± 1 s.d. from 17 bees=1.70± 0.07·mm; vertical thoracic diameterdivided by two). The velocity amplitude p-p of the thoracicoscillations was VATx= 188·mm·s–1 (mean ± 1 s.d.=187.8±95.2·mm·s–1; N=15, n=120). When comparing the measured particlevelocity values to the theoretical values, the difficulties to describethe vibrating bee as a simple sound source become obvious(Fig.·A1). Considering the bee’s thorax as simple monopole sourceoverestimates the measured values, and considering it as simpledipole source underestimates them.

Regressions calculated from measured valuesThe closest possible distance between the USP-probe and thevibrating bee was 5·mm, which prevented the tethered individualsfrom getting of the sensors and damage them. Therefore, theamplitudes of air particle velocity at still closer distances (1, 2, 3and 4·mm) had to be extrapolated using a regression analysis(Regression wizard, SigmaPlot 2001, SPSS Inc., USA). We appliedtwo hyperbolic decay functions (Fig.·A1) that were mathematicallyclosest to the equations for simple monopole sources (compareEqn·A6 and Eqn·A11) or simple dipole sources (compare Eqn·A10and Eqn·A12).

where VAd is the air particle velocity (p-p) at distance d and x andy are function variables, calculated by the regression analysis throughiteration.

The function variables (x, y), calculated by the regressionanalysis, should therefore represent the velocity amplitude of thethorax (VATx) and the radius a of the sound source. For the

xy3

(y+d)3 VAd = (A12) ,

xy

y+d VAd = (A11) ,

100

10

1

0.1

s–1)

mm(

AV

Monopole source

Dipole source

0 5 10 15 20

Distance to thorax (mm)

25

Fig.·A1. Theoretical and measured radiation of sound from the thorax of abee. Line graphs represent particle velocity (VA) as a function of thedistance from the thorax, which was assumed to be a monopole source(continuous line) or a dipole source (broken line). Open circles, means (± 1s.d.) of the particle velocities determined experimentally above the thorax inthe present study. Hyperbolic decay functions (hyperbolic decay 1, red line;hyperbolic decay 2, blue line) were calculated from the measured valuesthrough regression analysis.



hyperbolic decay function 1 (Eqn·A11), the variables were:x=556 (=VATx) and y=0.09 (=a). For the hyperbolic decay function2 (Eqn·A12) the variables were: x=63 (=VATx) and y=6.26 (=a).

As can be seen from these values, decay function 1 demands athoracic vibration velocity almost three times stronger than theactual value measured (and a source radius about 20 timessmaller), and decay function 2 one that is three times weaker(sound source 4� bigger). Therefore, even if both appliedregression functions fit well to the measured particle velocity atdistances >5·mm from the vibrating bee (regression coefficients:R2=70% and 78%), they not necessarily result in reasonable valuesat distances closer than 5·mm.

To assess the quality of the fit between our data and theregression functions at distances between 1·mm and 5·mm fromthe vibrating bee, we used data of preliminary experiments madein March 2005 with M. scutellaris and M. seminigra. Theparticle–velocity-sensor distances to the vibrating bee had thenincautiously been chosen to be 1, 2, 3, 5 and 10·mm, which ledto the damage of the sensor by the bees. However, the few resultsnevertheless received were now compared to the mathematicalfunctions derived from the present study (Fig.·A2). Both appliedregressions fit well to either the horizontally or the verticallyoriented particle velocities (Fig.·2A). Whereas the hyperbolicdecay 1 (Eqn·A11) describes well the vertically oriented particlevelocities, the hyperbolic decay 2 (Eqn·A12) is more appropriatefor the description of the horizontally oriented particle velocitiesat close distances (�1·mm). In the present study we, therefore,used the hyperbolic decay 1 (which is mathematically similar tothe decay around a monopole source) to calculate verticalparticle velocities at distances between 1 and 4·mm from thevibrating bee, and hyperbolic decay 2 (mathematically similarto the decay around a dipole source) to calculate the horizontalparticle velocities at these distances. However, since it isimpossible to describe air particle velocities very close to avibrating thorax with simple mathematical functions, particlevelocities for distances <1·mm from the vibrating bee were notcalculated.

APPENDIX 2

Parameters for hyperbolic decay functions calculated for the particle velocity above and around a bee at the respective direction relative tothe intact or wingless bee

Intact Wingless

Direction x y R2 (%) x y R2 (%)

Above beeVertically oriented* He 189 0.14 55 175 0.16 53

Tx 597 0.08 68 556 0.09 69Wt/Abd 1084 0.06 69 336 1.36 58

Around beeVertically oriented* (i) 11 2.26 82 9 3.31 76

(ii) 29 0.69 82 13 2.03 73(iii) 333 0.07 88 54 0.46 72(iv) 66 0.36 83 56 0.43 72(v) 101 0.23 72 8 3.69 66(vi) 327 0.08 72 14 1.65 76

Horizontally oriented** (i) 27 10.48 76 15 16.28 76(ii) 13 15.98 75 13 15.94 72(iii) 12 14.98 81 9 22.08 69(iv) 13 14.99 79 9 23.18 68(v) 11 16.93 67 9 20.69 75(vi) 13 15.97 78 8 24.20 77

He, above head; Tx, above thorax; Wt/Abd, above wingtips or abdomen; around the bee (i-vi), see Fig.·1B.Decay functions: *VAd=xy/y+d; **VAd=xy3/(y+d)3 (see Appendix 1). VAd, particle velocity, p-p, at distance d; x, y: function variables.

40

30

20

10

0

20

15

10

5

00 5 10 0 5 10

Distance to thorax (mm)

s–1)

mm(

p-p

AV

A

B

C

D

Horizontal Vertical

Direction vi

Direction vi(wingless)

Direction i

Direction vi

Fig.·A2. Extrapolation of air particle velocities close to a bee fromexponential decay functions. Horizontally oriented particle velocity in frontof a bee (A) and behind a bee (B); vertically oriented particle velocitybehind an intact individual (C) and behind a vibrating bee without wings(D). Measurements were made at 1, 3, 5 and 10·mm distance to vibratingindividuals of M. seminigra (open diamonds; A, N=2, single values shown;C, N=5), and at 1 and 2·mm distance to vibrating M. scutellaris (opencircles; B, N=5; C, N=5; D, N=4). The values (means ± 1 s.d.) aresuperimposed onto respective measurements in M. scutellaris (filled circles;N=12) and the resulting exponential decay functions (hyperbolic decay 1,red lines; hyperbolic decay 2, blue lines). Some symbols are slightlydisplaced horizontally for better visibility.


We would like to thank Luci Rolandi Bego and Ana Carolina Roselino for kindlymaking the colonies of M. scutellaris available. We also thank Christian Klopschand Karina Jorke for comparing the USP-probe measurements with the PIVmeasurements, and Hans-Elias de Bree (Microflown Technologies) for informationand discussions about the MicroflownTM USP-sensor. The experiments complywith the current laws of Brazil, where they were performed. This study wassupported by FWF grant P17530 to F.G.B. M.H. is currently supported byFAPESP grants 06/50809-7 and 06/53839-4.

REFERENCESAnderson, C. and Ratnieks, F. L. W. (1999). Worker allocation in social insect

societies: coordination of nectar foragers and nectar receivers in honey bee (Apismellifera) colonies. Behav. Ecol. Sociobiol. 46, 73-81.

Biesmeijer, J. C., van Nieuwstadt, M. G. L., Lukács, S. and Sommeijer, M. J.(1998). The role of internal and external information in foraging decisions ofMelipona workers (Hymenoptera: Meliponinae). Behav. Ecol. Sociobiol. 42, 107-116.

Dreller, C. and Kirchner, W. H. (1993). Hearing in honeybees: localization of theauditory sense organ. J. Comp. Physiol. A 173, 275-279.

Esch, H. (1961). Über die Schallerzeugung beim Werbetanz der Honigbiene. Z. Vergl.Physiol. 45, 1-11.

Esch, H. (1967). Die Bedeutung der Lauterzeugung für die Verständigung derstachellosen Bienen. Z. Vergl. Physiol. 56, 199-220.

Heinrich, B. (1993). The Hot-blooded Insects: Strategies and Mechanisms ofThermoregulation. Berlin, Heidelberg: Springer-Verlag.

Heran, H. (1959). Wahrnehmung und Regelung der Flugeigengeschwindigkeit bei Apismellifica L. Z. Vergl. Physiol. 42, 103-163.

Hrncir, M. (2003). Properties and significance of recruitment signals in a stingless bee(Melipona seminigra Friese 1903). PhD thesis, University of Vienna, Austria.

Hrncir, M., Jarau, S., Zucchi, R. and Barth, F. G. (2000). Recruitment behavior instingless bees, Melipona scutellaris and M. quadrifasciata. II. Possible mechanismsof communication. Apidologie 31, 93-113.

Hrncir, M., Jarau, S., Zucchi, R. and Barth, F. G. (2004a). Thorax vibrations instingless bees (Melipona seminigra). I. No influence of visual flow. J. Comp. Physiol.A 190, 539-548.

Hrncir, M., Jarau, S., Zucchi, R. and Barth, F. G. (2004b). Thorax vibrations instingless bees (Melipona seminigra). II. Dependence on sugar concentration. J.Comp. Physiol. A 190, 549-560.

Hrncir, M., Barth, F. G. and Tautz, J. (2006a). Vibratory and airborne sound-signalsin bee communication. In Insect Sounds and Communication: Physiology, Behaviour,Ecology, and Evolution (ed. S. Drosopoulos and M. Claridge), pp. 421-436. BocaRaton, London, New York: CRC Press, Taylor & Francis Group.

Hrncir, M., Schmidt, V. M., Schorkopf, D. L. P., Jarau, S., Zucchi, R. and Barth, F.G. (2006b). Vibrating the food receivers: a direct way of signal transmission instingless bees (Melipona seminigra). J. Comp. Physiol. A 192, 879-887.

Hrncir, M., Gravel, A. I., Schorkopf, D. L. P., Schmidt, V. M., Zucchi, R. and Barth,F. G. (2008). Thoracic vibrations in stingless bees (Melipona seminigra): resonancesof the thorax influence vibrations associated with flight but not those associated withsound production. J. Exp. Biol. 211, 678-685.

Jacobsen, F., Poulsen, T., Rindel, J. H., Gade, A. C. and Ohlrich, M. (2007).Fundamentals of Acoustics and Noise Control. Ørsted: DTU, Technical University ofDenmark.

King, M. J., Buchmann, S. L. and Spangler, H. (1996). Activity of asynchronous flightmuscle from two bee families during sonication (buzzing). J. Exp. Biol. 199, 2317-2321.

Lindauer, M. and Kerr, W. E. (1958). Die gegenseitige Verständigung bei denstachellosen Bienen. Z. Vergl. Physiol. 41, 405-434.

Michelsen, A. (1993). The transfer of information in the dance language of honeybees:progress and problems. J. Comp. Physiol. A 173, 135-141.

Michelsen, A. (2003). Signals and flexibility in the dance communication ofhoneybees. J. Comp. Physiol. A 189, 165-174.

Michelsen, A., Kirchner, W. H. and Lindauer, M. (1986). Sound and vibrationalsignals in the dance language of the honeybee, Apis mellifera. Behav. Ecol.Sociobiol. 18, 207-212.

Michelsen, A., Towne, W. F., Kirchner, W. H. and Kryger, P. (1987). The acousticnear field of a dancing honeybee. J. Comp. Physiol. A 161, 633-643.

Morawetz, L. (2007). Reichweite und Übertragung vibratorischer Signale bei derKommunikation stachelloser Bienen. Diploma thesis, University of Vienna, Austria.

Morawetz, L., Hrncir, M., Zucchi, R. and Barth, F. G. (2007). Propagation ofvibrational signals in the nest structures of a stingless bee (Melipona bicolor). InProceedings of 10th Meeting Austrian Neuroscience Association, Seggau, Austria,p. 26.

Morse, P. M. (1981). Vibration and Sound (4th edn). Woodbury, NY: American Instituteof Physics of the Acoustical Society of America.

Nieh, J. C. (1998). The recruitment dance of the stingless bee, Melipona panamica.Behav. Ecol. Sociobiol. 43, 133-145.

Nieh, J. C., Contrera, F. A. L., Rangel, J. and Imperatriz-Fonseca, V. L. (2003).Effect of food location and quality on recruitment sounds and success in twostingless bees, Melipona mandacaia and Melipona bicolor. Behav. Ecol. Sociobiol.55, 87-94.

Schneider, P. (1975). Versuche zur Erzeugung des Verteidigungstones bei Hummeln.Zool. Jb. Physiol. 79, 111-127.

Snodgrass, R. E. (1956). Anatomy of the Honey Bee. Ithaca, NY: Cornell UniversityPress.

Sokal, R. R. and Rohlf, F. J. (1995). Biometry (3rd edn). New York: Freeman.Tsujiuchi, S., Sivan-Loukianova, E., Eberl, D. F., Kitagawa, Y. and Kadowaki, T.

(2007). Dynamic range compression in the honey bee auditory system towardwaggle dance sounds. PLoS ONE 2, e234.

Wenner, A. M. (1962). Sound production during the waggle dance of the honeybee.Anim. Behav. 10, 79-95.

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The sound field generated by tethered stingless bees ...jeb.biologists.org/content/jexbio/211/5/686.full.pdf · bee foragers of the genus Melipona generate pulsed thorax vibrations